Basically, all of them. Bookmarks, passwords, open tabs and named windows.
I think that web-browsers have become OSes in themselves (no pun intented at Chrome). So, when switching from my desktop to my laptop, I'd like my browser to move with me in its entirity. If I have configured a personal profile, a work profile, and a finance profile on my desktop, I wouldn't want to have to reconfigure them on my laptop.
Caution: I do think that with Profiles, Named Windows, and Containers/Sessions, we do run into a risk of feature bloat. They're all very similar -- not the same but similar.